On The Stability of Graph Convolutional Neural Networks Under Edge Rewiring

Kenlay, Henry; Thano, Dorina; Dong, Xiaowen

doi:10.1109/icassp39728.2021.9413474

“…Maskey et al (2022) proved the stability of the spatial-based message passing. Kenlay et al (2020Kenlay et al ( , 2021a proved the stability for the spectral GCNs.…”

Section: Stability Of Graph Convolutionsmentioning

confidence: 92%

Framelet Message Passing

Liu¹,

Zhou²,

Zhang³

et al. 2023

Preprint

0

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Graph neural networks (GNNs) have achieved champion in wide applications. Neural message passing is a typical key module for feature propagation by aggregating neighboring features. In this work, we propose a new message passing based on multiscale framelet transforms, called Framelet Message Passing. Different from traditional spatial methods, it integrates framelet representation of neighbor nodes from multiple hops away in node message update. We also propose a continuous message passing using neural ODE solvers. It turns both discrete and continuous cases can provably achieve network stability and limit oversmoothing due to the multiscale property of framelets. Numerical experiments on real graph datasets show that the continuous version of the framelet message passing significantly outperforms existing methods when learning heterogeneous graphs and achieves state-of-the-art performance on classic node classification tasks with low computational costs.

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“…The simple GCN (SGCN) [14] is motivated by considering a multilayered GCN with an affine approximation of graph convolution filter and the removal of activation functions between layers. By simplifying a GCN in [15] with K layers, the graph filter in SGCN can be represented by keeping only the Kth order GSO in (1), so the output of the filter is y = h K S K x = h(S)x and the output of a SGCN with a single linear logistic regression layer is…”

Section: The Stability Of Sgcnmentioning

confidence: 99%

Graph Neural Network Sensitivity Under Probabilistic Error Model

Wang¹,

Ollila²,

Vorobyov³

2022

Preprint

0

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Graph convolutional networks (GCNs) can successfully learn the graph signal representation by graph convolution. The graph convolution depends on the graph filter, which contains the topological dependency of data and propagates data features. However, the estimation errors in the propagation matrix (e.g., the adjacency matrix) can have a significant impact on graph filters and GCNs. In this paper, we study the effect of a probabilistic graph error model on the performance of the GCNs. We prove that the adjacency matrix under the error model is bounded by a function of graph size and error probability. We further analytically specify the upper bound of a normalized adjacency matrix with self-loop added. Finally, we illustrate the error bounds by running experiments on a synthetic dataset and study the sensitivity of a simple GCN under this probabilistic error model on accuracy.

show abstract

“…The simple GCN (SGCN) [15] is motivated by considering a multilayered GCN with an affine approximation of graph convolution filter and the removal of activation functions between layers. By simplifying a GCN in [16] with K layers, the graph filter in SGCN can be represented by keeping only the Kth order GSO in (1), so the output of the filter is y = h K S K x = h(S)x and the output of a SGCN with a single linear logistic regression layer is…”

Section: The Stability Of Sgcnmentioning

confidence: 99%

Graph Neural Network Sensitivity Under Probabilistic Error Model

Wang

¹

,

Ollila

²

,

Vorobyov

³

2022

2022 30th European Signal Processing Conference (EUSIPCO)

0

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Graph convolutional networks (GCNs) can successfully learn the graph signal representation by graph convolution. The graph convolution depends on the graph filter, which contains the topological dependency of data and propagates data features. However, the estimation errors in the propagation matrix (e.g., the adjacency matrix) can have a significant impact on graph filters and GCNs. In this paper, we study the effect of a probabilistic graph error model on the performance of the GCNs. We prove that the adjacency matrix under the error model is bounded by a function of graph size and error probability. We further analytically specify the upper bound of a normalized adjacency matrix with self-loop added. Finally, we illustrate the error bounds by running experiments on a synthetic dataset and study the sensitivity of a simple GCN under this probabilistic error model on accuracy.

show abstract

On The Stability of Graph Convolutional Neural Networks Under Edge Rewiring

Cited by 19 publications

References 17 publications

Framelet Message Passing

Framelet Message Passing

Graph Neural Network Sensitivity Under Probabilistic Error Model

Graph Neural Network Sensitivity Under Probabilistic Error Model

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